Z.H. Wang

Bio: Z.H. Wang is an academic researcher from Nanjing University of Aeronautics and Astronautics. The author has contributed to research in topics: Rotor (electric) & Boundary value problem. The author has an hindex of 6, co-authored 10 publications receiving 283 citations.

Stability switches of time-delayed dynamic systems with unknown parameters

Abstract: The paper presents a systematic method of stability analysis for high-dimensional dynamic systems involving a time delay and some unknown parameters. Here, the term “unknown” means that the parameters are constants but yet to be determined. The analysis focuses on the stability switches of those systems with increase of the time delay from zero to infinity. On the basis of the generalized Sturm criterion, the parameter space of concern is divided into several regions determined by a discrimination sequence and the Routh–Hurwitz conditions. It is found, as the time delay increases, that the system may undergo no stability switch, exactly one stability switch, or more than one stability switches when the parameters are chosen from different regions. To demonstrate the approach, a detailed analysis of the stability switches is made in the paper for an active vehicle suspension equipped with a delayed “sky-hook” damper and a four-wheel steering vehicle with time delay in driver's response, respectively.

Delay-independent stability of retarded dynamic systems of multiple degrees of freedom

Abstract: On the basis of generalized Sturm theory, this paper presents a simple, but systematic approach to the delay-independent stability analysis of the linear dynamic systems involving multiple degrees of freedom and possibly two time delays. The approach enables one to complete the stability analysis in a much simpler way than before through the use of a MAPLE routine given in the paper. To demonstrate the approach, the paper gives a detailed analysis, the corresponding sufficient and necessary conditions as well as stable regions in parameter space of concern for the delay-independent stability of a vibrating system with time delays in state feedback, an active-tendon for a tall structure and an active suspension of a quarter car model.

Stability analysis of damped sdof systems with two time delays in state feedback

Abstract: This paper presents the stability analysis of linear, damped SDOF vibration control systems with two time delays, one in the displacement feedback and the other in the velocity feedback. First, a sufficient and necessary algebraic criterion is proved to check the system stability independent of time delays. According to this criterion, all possible combinations of the feedback gains that guarantee the delay-independent stability are given. Then, the effect of the feedback gains on the system stability is discussed when the time delays are finite. The most dangerous case is found when the time delay in the displacement feedback is much longer than that in the velocity feedback.

Calculation of the rightmost characteristic root of retarded time-delay systems via Lambert W function

Abstract: Generally, it is not easy to analyze the stability of time-delay systems, especially when the systems are of high order or they have multiple delays. For retarded time-delay systems, the stability can be determined by the rightmost characteristic root. This paper presents a case study on the calculation of the rightmost root. Three practical time-delay systems are discussed. The first system is an oscillator with delayed state feedback, the second one is a delayed neural network based on the FitzHugh–Nagumo model for neural cells, and the third one is a car model of suspension with a delayed sky-hook damper. By using the Lambert W function, the rightmost root becomes a root of a function associated with the principal branch of the Lambert W function. Then the rightmost root is located by using Newton–Raphson's scheme or Halley's accelerating scheme. Some suggestions for successful application of the proposed method are given.

Stabilization of vibration systems via delayed state difference feedback

Abstract: This paper presents a study of the stabilization problem, via delayed state feedback of Pyragas type, for unstable vibration systems that have even number of characteristic roots with positive real parts. On the basis of stability switches with respect to the time delay, a new stabilization criterion is established, and an effective procedure for determining the admissible values of the feedback gains and the delay is given. Two examples are given in detail to demonstrate the efficiency of the theory.

H∞ control of active vehicle suspensions with actuator time delay

Abstract: The paper deals with the H ∞ control problem for active vehicle suspension systems with actuator time delay The time delay for the actuator is assumed as uncertain time-invariant but has a known constant bound By suitably formulating the sprung mass acceleration, suspension deflection and tyre deflection as the optimization object and considering the actuator time delay, a delay-dependent memoryless state feedback H ∞ controller is designed in terms of the feasibility of certain delay-dependent matrix inequalities A quarter-car model with active suspension system is considered in this paper and a numerical example is employed to illustrate the effectiveness of the proposed approach It is confirmed by the simulations that the designed controller not only can achieve the optimal performance for active suspensions but also preserves the closed-loop stability in spite of the existence of the actuator time delay within allowable bound

Active Structural Vibration Control: A Review

Abstract: In this paper we review essential aspects in- volved in the design of an active vibration control system. We present a generic procedure to the design process and give selective examples from the literature on relevant ma- terial. Together with examples of their applications, various topics are briefly introduced, such as structure modeling, model reduction, feedback control, feedforward control, con- trollability and observability, spillover, eigenstructure assign- ment (pole placement), coordinate coupling control, robust control, optimal control, state observers (estimators), intelli- gent structure and controller, adaptive control, active con- trol effects on the system, time delay, actuator-structure interaction, and optimal placement of actuators.

Time-Delay Systems: Analysis and Control Using the Lambert W Function

Abstract: Time-Delay Systems Delay Differential Equations Lambert W Function Stability Controllability Observability Feedback Control Eigenvalue Assignment State Observer Chatter in Machining Human Immunodeficiency Virus Diesel Engine Control Robust Control Time-Domain Specification

Stability switches of time-delayed dynamic systems with unknown parameters

Abstract: The paper presents a systematic method of stability analysis for high-dimensional dynamic systems involving a time delay and some unknown parameters. Here, the term “unknown” means that the parameters are constants but yet to be determined. The analysis focuses on the stability switches of those systems with increase of the time delay from zero to infinity. On the basis of the generalized Sturm criterion, the parameter space of concern is divided into several regions determined by a discrimination sequence and the Routh–Hurwitz conditions. It is found, as the time delay increases, that the system may undergo no stability switch, exactly one stability switch, or more than one stability switches when the parameters are chosen from different regions. To demonstrate the approach, a detailed analysis of the stability switches is made in the paper for an active vehicle suspension equipped with a delayed “sky-hook” damper and a four-wheel steering vehicle with time delay in driver's response, respectively.

Parameter-dependent input-delayed control of uncertain vehicle suspensions

Abstract: This paper presents a parameter-dependent controller design approach for vehicle active suspensions to deal with changes in vehicle inertial properties and existence of actuator time delays. By defining a parameter-dependent Lyapunov functional, matrix inequality conditions with reduced conservatism are obtained for the design of controllers. Feasible solutions can be obtained by solving a finite number of linear matrix inequalities (LMIs) embedded within a genetic algorithm (GA). Both state feedback and static output feedback controllers can be designed under a unified framework. Based on the measurement or estimation of the vehicle inertial parameters, a parameter-dependent controller could be implemented in practice. The presented approach is applied to a two-degree-of-freedom quarter-car suspension model. Numerical simulations on both bump and random road responses show that the designed parameter-dependent controllers can achieve good active suspension performance regardless of the variation on the sprung mass and the presence of actuator time delay.